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Expansion of (1-25*x)^(-7/5).
2

%I #19 Sep 08 2022 08:44:58

%S 1,35,1050,29750,818125,22089375,589050000,15567750000,408653437500,

%T 10670395312500,277430278125000,7187966296875000,185689129335937500,

%U 4785066025195312500,123044554933593750000,3158143576628906250000

%N Expansion of (1-25*x)^(-7/5).

%H Robert Israel, <a href="/A049395/b049395.txt">Table of n, a(n) for n = 0..713</a>

%F G.f.: (1-25*x)^(-7/5).

%F a(n) = (5^n/n!) * Product_{k=0..n-1} (5*k+7).

%F a(n) ~ 5/2*Gamma(2/5)^-1*n^(2/5)*5^(2*n)*{1 + 7/25*n^-1 - ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001

%F a(n) = (25+10/n)*a(n-1) for n >= 1. - _Robert Israel_, Mar 15 2020

%p f:= gfun:-rectoproc({a(n) = (25+10/n)*a(n-1), a(0) = 1}, a(n), remember):

%p map(f, [$1..50]); # _Robert Israel_, Mar 15 2020

%t CoefficientList[Series[(1-25*x)^(-7/5), {x, 0, 15}], x] (* _Georg Fischer_, Jan 16 2020 *)

%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 16); Coefficients(R!( (1-25*x)^(-7/5) )); // _Marius A. Burtea_, Jan 16 2020

%Y Cf. A049380.

%K nonn,easy

%O 0,2

%A Joe Keane (jgk(AT)jgk.org)

%E Typo in name corrected by _Georg Fischer_, Jan 16 2020